Solve (2/3)^-2/6^-1+7^0

$$\frac { ( \frac { 2 } { 3 } ) ^ { - 2 } } { 6 ^ { - 1 } + 7 ^ { 0 } }$$

Evaluate

$$\frac{27}{14}\approx 1.928571429$$

Solution Steps

Calculate \frac{2}{3} to the power of -2 and get \frac{9}{4}.

$$\frac{\frac{9}{4}}{6^{-1}+7^{0}}$$

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\frac{\frac{9}{4}}{\frac{1}{6}+7^{0}}$$

Calculate 7 to the power of 0 and get 1.

$$\frac{\frac{9}{4}}{\frac{1}{6}+1}$$

Add \frac{1}{6} and 1 to get \frac{7}{6}.

$$\frac{\frac{9}{4}}{\frac{7}{6}}$$

Divide \frac{9}{4} by \frac{7}{6} by multiplying \frac{9}{4} by the reciprocal of \frac{7}{6}.

$$\frac{9}{4}\times \frac{6}{7}$$

Multiply \frac{9}{4} and \frac{6}{7} to get \frac{27}{14}.

$$\frac{27}{14}$$

Factor

$$\frac{3 ^ {3}}{2 \cdot 7} = 1\frac{13}{14} = 1.9285714285714286$$